The state of the system is given by \(\Psi =\underline{\psi }_{\overline{N}_{1}N_{2}}\) ,
then it has non-zero transition probability for several
other processes; that is, upon interaction with the surrounding
matter fields, the initial state \(\underline{\psi }_{\overline{N}_{1}N_{2}}\) 
can make a quantum jump to the start of another event \(\underline{\psi }_{\overline{N}_{n+1}N_{n+2}}\) 
via an elementary, “would be compound” process \(\mathsf {e}_{\gamma _{\overline{N}_{1}\overline{N}_{n}}N_{n+1}}\) ,
which may even lie in a different curve \(\gamma ^{\prime }\)  (see next
figure), and this is the physical interpretation we give to \(\mathcal {P}_{\mathsf {e}_{\overline{N}_{1}N_{2}}\rightarrow \mathsf {e}_{\overline{N}_{n+1}N_{n+2}}^{start}}(\mathrm {a}(\gamma _{\overline{N}_{2}\overline{N}_{n}},P_{N_{n+1}}))_{\alpha _{\frac{1}{2}},A_{\mu }}\) .
We also note that, unlike the classical case, we don't need to introduce
change in an ad-hoc manner here, since change can be seen as arising
from quantum collapseWhich, for more precision, we define as the abrupt jump from one state
to another after an interaction, if one accepts that Quantum Theory
is a complete theory, or as the abrupt change in the values, if one
doesn't accept that and, instead, introduces contextual hidden variables
(which give us the values.) (now taken as ontologically fundamentalThis is the case, for example, in Rovelli's Relational Interpretation
[1]}, which, then, seems very well suited for this approach. and irreducible) after an interaction. We take the collapse
as the only source of change and actually identify it
with it (in other views, collapse, of course, implies change, but
the converse is not necessary; here we say they are indeed the same
thing.) Thus, the change in the classical theory actually comes from
the fundamental quantum theory, of which the former is a limit. Furthermore,
in light of this, then the argument used to show the necessity of
the collapse in QM can be now used to show the necessity of change,
which then becomes a quantum phenomena and very tied to the characteristic
non-commutativity of quantum properties.
